How to make custom logo for published bge game
This is not really a question about Blender itself, but additionally to the answers provided in the question linked above you can also make a launcher application to start you game and run it from there.

The launcher application can then have any custom icon you want.

Just create a batch file to start the game with the command
start path/to/game.exe

and use some application like Bat to EXE to compile it into an executable. That executable can then have any icon file you want